Expected Utility for Queues Servicing Messages with Exponentially Decaying Utility

Abstract

assumes a greater importance than in other queueing problems. We consider here a single queue of this sort, and, with some distribution-theoretic restrictions, derive expressions for the expected (terminal) utility in two cases: (a) most recent, and (b) least recent message serviced first, with both random and regular departures. 2. Assumptions. Consider a single queue of messages, in equilibrium, and assume that each message has associated with it at time t after entry, a utility subject to exponential decay. We investigate the loss of utility due to queueing delay in several different circumstances. In each case X denotes the mean arrival rate, IA the mean departure rate, p = X/ji. No messages are removed from the queue without completion of service. If the initial utility of a message (at the time of entry into the queue) is denoted by yo, the waiting time in the queue (exclusive of service time) by w and the final utility (when entering service) by y, then we assume yo and w to be independent random variables, with